Keywords: Comparative effectiveness research, Instrumental variable, Missing survival time, Observational study, Simultaneous equations model, Survival analysis
Consistent estimation of the effect of a treatment in the presence of unmeasured confounding is a common objective in observational studies. The Two Stage Least Squares (2SLS) Instrumental Variables (IV) procedure is frequently used but not applicable to time-to-event data with some observations censored. We develop a statistical method to account for unmeasured confounding of the effect of treatment on survival endpoints subject to censoring by considering censoring and confounding in sequence. We first jointly model survival time and treatment using a simultaneous equations model (SEM) under a specific bivariate distribution for the underlying data generating process. The joint model is used for the sole purpose of imputing the censored survival times. Then we apply an IV procedure to the completed dataset. This two-phase approach allows censoring to be accounted while preserving the robustness of the IV method to distributional miss-specifications in the joint model. The approach can be applied to any type of survival outcome including continuous and fixed-time endpoints. The methodology is illustrated on two examples of a vascular surgery study and a mental health study.